Acceleration of the Inversion of Triangular Toeplitz Matrices and Polynomial Division

Computing the reciprocal of a polynomial in z modulo a power z(n) is well known to be closely linked to polynomial division and equivalent to the inversion of an n x n triangular Toeplitz matrix. The degree k of the polynomial is precisely the bandwidth of the matrix, and so the matrix is banded iff k << n. We employ the above equivalence and some elementary but novel and nontrivial techniques to obtain minor yet noticeable acceleration of the solution of the cited fundamental computational problems.